1991 AHSME Problems/Problem 23
Problem
If is a square, is the midpoint of , is the midpoint of , and intersect at , and and intersect at , then the area of quadrilateral is
Solution 1: Coordinate Geometry
Solution by e_power_pi_times_i
First, we find out the coordinates of the vertices of quadrilateral , then use the Shoelace Theorem to solve for the area. Denote as . Then . Since I is the intersection between lines and , and since the equations of those lines are and , . Using the same method, the equation of line is , so . Using the Shoelace Theorem, the area of is .
See also
1991 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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